I don't know about UK but the two most popular I see are Dylon dyes and rit dyes. I've used Dylon on a shirt before and it worked well enough. I dyed a white shirt navy and it came out very even and the colour hasn't washed out at all.
Ask for both! I asked for Chesnut and Cinnamon laces when I put my bison boot order in and couldnt decide which would look better, Rancourt was more than happy to send me a second set of laces for free.